# Phase velocity of an electron with kinetic energy of 5eV and 50keV

1. Mar 25, 2008

### beramodk

1. The problem statement, all variables and given/known data
Consider electrons of kinetic energy 5eV and 500keV. For each electron, what would be the
particle speed, phase velocity, group velocity, and Broglie wavelength?

2. Relevant equations
lambda = h/p (lambda = broglie wavelength)
K.E. for nonrelativistic calcualtion = p^2/(2m)
phase velocity = lambda*f = lambda / time
group velocity = dw/dk

3. The attempt at a solution
So for the 5eV case, I found that since the energy is low, i can use non-relativistic calculation. I find the Broglie wavelength to be around 0.548 nm and the momentum to be 1.208E-24 kg(m/s). Knowing the momentum, I used p=mv to find the particle velocity, which came out to be around 1.326E6 m/s.

So far I think I am doing it right, but I cannot find the phase velocity nor the group velocity. Something tells me that for a non-relativistic case, the phase velocity is equal to c and the group velocity is equal to the particle speed. Can anyone explain this to me?

Also, how should I approach the 50keV electron case, since the energy is so high I need to use relativity.

Thanks.

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